Question

Which of the following is a point on the graph as described by the function y = (2z + 1)' - 4?
(1 point)

O (-1,-5)
O (1,2)
O (0,-2)
O (-1,-3)

Answer 1

To determine which of the given points is on the graph of the function \( y = (2z + 1) - 4 \), we first need to simplify the function. The ' indicates differentiation, and it's a little unclear in this context, so let’s treat it simply as the expression given rather than perform differentiation.

Thus, the function can be rewritten as:

\[
y = 2z + 1 - 4
\]

Simplifying this gives:

\[
y = 2z - 3
\]

Next, we can check each point to see if it satisfies this equation.

1. For the point \((-1, -5)\):
\[
y = 2(-1) - 3 = -2 - 3 = -5 \quad \text{(this point lies on the graph)}
\]

2. For the point \((1, 2)\):
\[
y = 2(1) - 3 = 2 - 3 = -1 \quad \text{(this point does NOT lie on the graph)}
\]

3. For the point \((0, -2)\):
\[
y = 2(0) - 3 = 0 - 3 = -3 \quad \text{(this point does NOT lie on the graph)}
\]

4. For the point \((-1, -3)\):
\[
y = 2(-1) - 3 = -2 - 3 = -5 \quad \text{(this point does NOT lie on the graph)}
\]

From this analysis, only the point \((-1, -5)\) satisfies the equation \( y = 2z - 3 \).

The correct answer is:

**O (-1,-5)**